Question 705014

SCQMEDIUM

Canals A and B join to form canal C, all having semi-circular cross-sections of radii which are in the ratio $3:4:5$ , respectively. Assume smooth merger of A and B, and ignore the possibility of flooding. If the speed $s$ of water is the same and uniform in both A and B then the speed of water flowing in C is

(A)

$s$

(B)

$7s/5$

(C)

$2s$

(D)

$5s/7$

Detailed Solution

Area of semi-circle = $\frac{1}{2}\pi r^2$ . Total flow rate = $Area_A \times s + Area_B \times s = Area_C \times V$ . Given radii $r_A=3x, r_B=4x, r_C=5x$ .

$\frac{1}{2}\pi(3x)^2 s + \frac{1}{2}\pi(4x)^2 s = \frac{1}{2}\pi(5x)^2 V$ . $9x^2 s + 16x^2 s = 25x^2 V$ . $25x^2 s = 25x^2 V \implies V = s$ .

Free Exam

Boost Your Exam Preparation!

Move beyond just reading solutions. Access our comprehensive Test Series, original Mock Tests, and interactive learning modules. Many premium tests are completely free!

Original Mocks & Regular Test Series
Real NTA-like Interface with Analytics
Many Free Tests Available